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http://dx.doi.org/10.14317/jami.2014.707

SUPERCONVERGENCE AND A POSTERIORI ERROR ESTIMATES OF VARIATIONAL DISCRETIZATION FOR ELLIPTIC CONTROL PROBLEMS  

Hua, Yuchun (Department of Mathematics and Computational Science, Hunan University of Science and Engineering)
Tang, Yuelong (Department of Mathematics and Computational Science, Hunan University of Science and Engineering)
Publication Information
Journal of applied mathematics & informatics / v.32, no.5_6, 2014 , pp. 707-719 More about this Journal
Abstract
In this paper, we investigate a variational discretization approximation of elliptic optimal control problems with control constraints. The state and the co-state are approximated by piecewise linear functions, while the control is not directly discretized. By using some proper intermediate variables, we derive a second-order convergence in $L^2$-norm and superconvergence between the numerical solution and elliptic projection of the exact solution in $H^1$-norm or the gradient of the exact solution and recovery gradient in $L^2$-norm. Then we construct a posteriori error estimates by using the superconvergence results and do some numerical experiments to confirm our theoretical results.
Keywords
Finite element methods; optimal control problems; convergence; superconvergence; a posteriori error estimates;
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Times Cited By KSCI : 1  (Citation Analysis)
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